Module #17. Work/Strain Hardening. READING LIST DIETER: Ch. 4, pp ; Ch. 6 in Dieter

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Module #17. Work/Strain Hardening. READING LIST DIETER: Ch. 4, pp. 138-143; Ch. 6 in Dieter"

Transcription

1 Module #17 Work/Strain Hardening READING LIST DIETER: Ch. 4, pp ; Ch. 6 in Dieter D. Kuhlmann-Wilsdorf, Trans. AIME, v. 224 (1962) pp

2 Work Hardening RECALL: During plastic deformation, dislocation density increases. We ve addressed this earlier. It is this increase in dislocation density that ultimately leads to work hardening. Dislocations interact with each other and can assume configurations that restrict the movement of other dislocations. The situation gets more severe as the dislocation density increases leading to an increase in the flow stress. [Ashby, Shercliff, & Cebon, p. 129] The dislocations can be either strong or weak obstacles depending upon the types of interactions that occurs between moving dislocations.

3 Work Hardening (2) To properly discuss work hardening, let s first consider the plastic deformation of a single crystal. F A o Plastic deformation is initiated at a critical stress, the critical resolved shear stress (CRSS). Recall from our derivation of the Taylor-Orowan equation that this is the same stress at which dislocations begin to move on a specific slip system. Slip plane normal A s F Slip direction coscos CRSS ys

4 Single crystal deformation (1) The characteristic vs. curve for a single crystal oriented for slip on one slip system (i.e., single slip) is shown to the right. CRSS Stage III Stage I Stage II It can be sub-divided into three stages based on work hardening behavior. Stage I: EASY GLIDE After yielding, shear stress for plastic deformation is almost constant. There is little or no work hardening. Typical of systems when single slip system is operative. Very few dislocation interactions: easy glide. Only interactions between the stress fields of dislocations to contend with. We mentioned this earlier. The active slip system has a maximum Schmid factor.

5 Single crystal deformation (2) Stage I: Conceptual description of easy glide Consider an array of dislocations moving on parallel slip planes. We ll use edge dislocations for schematic purposes. Edge dislocations have compressive stress fields above the slip plane and tensile stress fields below the slip plane. CRSS Stage I Stage III Stage II compression These stress fields interact during the early stages of deformation resulting in weak drag effects. Think of it as a friction force that inhibits glide. This frictional effect will increase as dislocation density increases. tension This is schematically illustrated to the right. You should consider how this relates to our prior discussions of dislocation configurations and the Peierls-Nabarro model for slip. Slip planes Attractive force In stage I dislocations are weak obstacles. Repulsive force

6 Single crystal deformation (3) Stage II: LINEAR HARDENING needed to continue plastic deformation begins to increase. This increase is approximately linear. Linear hardening. This stage begins when slip occurs on multiple slip systems. The work hardening rate increases due to interactions between dislocations moving on intersecting planes. This results in the production of jogs and other sessile dislocation configurations such as Lomer-Cottrell Locks, etc. CRSS Stage I Stage II More about Stage II on the next viewgraph Stage III Stage III: PARABOLIC HARDENING See a decreasing rate of work hardening due to an increase in the degree of cross slip. This is called parabolic hardening. Have a parabolic shape to the curve. NOTE: Polycrystals often go straight into stage III. Why?

7 Single crystal deformation (4) Stage II: Dislocation tangles ( forest dislocations ) form strong obstacles to dislocation motion. CRSS Stage I Stage II Stage III Tangles form when dislocation motion leads to the formation of immobile dislocation segments. Those segments will keep other dislocations from moving freely. Work hardening depends strongly on dislocation density: line length L unit volume L 1 L 3 2 The average separation distance between dislocations is: L constant Interactions can produce immobile dislocation configurations. Examples include Jogs and sessile dislocation locks (e.g., Lomer or Lomer-Cottrell locks).

8 Single crystal deformation (6) Recall the general hardening law : Stage III max Gb L CRSS Stage I Stage II If we substitute our expression for L into the equation above, we can express the shear flow stress as: o Gb where: o intrinsic flow strength for free material constant (0.2 for FCC, 0.4 for BCC) The strengthening increment derived from work hardening can now be approximated as: Gb or MGb k L constant G.I. Taylor, Proceedings of the Royal Society, A145, pp In this equation, M is the Taylor factor. G must be converted to E.

9 Single crystal deformation (7) Note for both materials (in this case Ti and Cu) that the stress ( and ) exhibits a ( ) ½ dependence Ti Cu FIGURE CRSS versus for Cu single crystals and polycrystals. - polycrystal; - single crystal, one slip system; - single crystal, two slip systems; - single crystal, six slip systems. [Image scanned from Courtney's text. Originally from H. Weidersich, J. Metals, 16 (1964) 425] FIGURE Flow stress versus for different grades of Ti deformed at room temperature. [R.L. Jones and H. Conrad, Trans. AIME, 245 (1969) ] Strength

10 Dislocation microstructure as function of p and Low strain: somewhat random. High strain: dense tangles and cellular arrangements. Form near the end of Stage II in single crystals. Cell boundaries have high. Cell interiors have low. Cells are called subgrains. Polycrystalline 304 Stainless steel Why do they form? Is strength still proportional to? Figure adapted from J.R. Foulds, A.M. Ermi, and J. Moteff, Materials Science and Engineering, 45 (1980) This journal paper provides a nice description of how dislocation microstructures evolve.

11 III II I CRSS Stage I Stage II Stage III I ~ G/10,000 This stage is often absent when multiple slip systems are operative II ~ G/300 Typical work hardening rates

12 Influence of crystal structure on single crystal stress-strain strain curves Shear Stress FCC (Cu) BCC (Nb) Stress-strain curves for three typical metallic crystal structures. Adapted from T. Suzuki, S. Takeuchi, and H. Yoshinaga, Dislocation Dynamics and Plasticity, Springer-Verlag, Berlin, 1991, p. 15. HCP (Mg) Shear Strain

13 In some crystal structures, dislocations dissociate to slip DOES THIS HAVE ANY IMPACT ON WORK HARDENING?

14 RECALL: Dissociation of unit dislocations in an FCC crystal In this example, the separation into partial dislocations is energetically favorable. There is a decrease in strain energy. A C B A ao 6 ao b ao 6 ao b ao 2 ao b C ao ao ao ao ao ao Separation produces a stacking fault between the partials. B

15 FCC Crystal STACKING FAULT Width = d SLIPPED A $ a o b B C $ $ a o D b UNSLIPPED ao 2 ao b SFE d G Gb2b3 SFE 2 d partial dislocation separation shear modulus AB represents a regular (un-extended) dislocation. BC and BD represent partial dislocations. The region between BC and BC represents the stacking fault. In this region, the crystal has undergone intermediate slip. BC + stacking fault + BD represents an extended dislocation. Extended dislocations (in particular screw dislocations) define a specific slip plane. Thus, extended screw dislocations can only cross-slip when the partial dislocations recombine. See the illustration on the next page. This process requires some energy.

16 Extended Dislocation [Partial Dislocation + SF + Partial Dislocation] An extended screw dislocation must constrict before it can cross slip. Schematic illustration Cross-slip plane (11 1) plane (1) Extended (2) Formation of constricted segment (111) plane (4) (3) Cross-slip of constricted segment and separation into extended b (1) (2) Direction of motion (3) (4) Slip of extended on cross-slip plane

17 Influence of partial dislocations and SFE on deformation High SFE higher strain hardening rate Low SFE lower strain hardening rate Wavy slip lines Straight slip lines Dislocation cells and tangles Planar dislocation arrangement (a) Cu having a high SFE and therefore essentially un-dissociated dislocations. Cross-slip leads to the wavy slip bands and tangled dislocations (b) Cu-7.5 wt.% Al alloy, having a low SFE and dissociated dislocations. The absence of cross-slip leads to straight slip traces and uniform dislocation lines. Figure 9-11 Comparison of the deformation of two types of uniform polycrystalline materials in stage II deformation. From Guy, Introduction to Materials, McGraw-Hill, New York (1972) p. 419 [originally in Johnston and Feltner, Metallurgical Transactions, v. 1, n. 5 (1970) pp ].

18 Effect of γ SFE on Deformation Mechanism-1 (for FCC crystals) High γ SFE SFE SFE Gb b 2 d 2 3 Wavy slip steps observed Dislocation cells and tangles Pure Cu Few partial dislocations or small d. Thus, it is easier for cross-slip to occur. Pure Cu Random distribution of dislocations is observed because dislocations are not confined to specific slip planes. They can cross slip to overcome obstacles. Figure 9-11 Comparison of the deformation of two types of uniform polycrystalline materials in stage II deformation. From Guy, Introduction to Materials, McGraw-Hill, New York (1972) p. 419 [originally in Johnston and Feltner, Metallurgical Transactions, v. 1, n. 5 (1970) pp ].

19 Effect of γ SFE on Deformation Mechanism-2 (for FCC crystals) Low γ SFE SFE SFE Gb b 2 d 2 3 Straight slip steps observed Dislocations seem to be confined to specific bands/planes Cu 7.5 wt.% Al Slip is confined to specific planes. Leads to straight slip lines/steps on surface. Lots of partials, large d makes cross slip difficult. Cu 7.5 wt.% Al Dislocation movement is restricted due to because cross slip is inhibited. RECALL: partials must recombine to cross slip. [Images from Guy, Introduction to Materials, McGraw-Hill, New York (1972) p.419]

20 Partial to Partial Dislocation separation distance vs. γ SFE partial SF partial d Table: Stacking-fault free energies and separation between Shockley partial dislocations for metals (θ = 30 ). SFE 2 Gbp 2 2 cos2 1 8d 1 2 Metal γ (mj/m 3 ) a o (nm) b (nm) G (GPa) d (nm) Al Cu If θ = 0, ν = 1/3 Au Ni Gbp d or d 5 SFE 1 SFE Ag Notice the big change in d with γ SFE Cross-slip easier when d is small γ SFE is high

21 FCC Crystal SLIPPED A $ It is more difficult to re-combine wide stacking faults (i.e., those with large d). Cross-slip is more difficult in materials with low SFE. Thus high SFE materials will work harden more rapidly. Material a o b B C ao 2 ao b SFE (mj/m 2 ) $ $ b Fault width Strain Hardening rate REASONS Stainless Steel <10 ~0.45 High Cross slip is more difficult Copper ~90 ~0.30 Med a o UNSLIPPED STACKING FAULT Width = d D Aluminum ~250 ~0.15 Low Cross slip is easier See pages in Hertzberg Gb2b3 SFE SFE 2 d d partial dislocation separation G shear modulus

22 Summary of hardening/strengthening mechanisms for crystalline solids Hardening Mechanism Nature of Obstacle Strong or Weak Hardening Law Work hardening Other dislocations Strong [1] Gb (see ) Grain size / Hall-Petch Grain boundaries Strong [2] ky d (see ) [3] 3/2 1/2 [4] Solid solution Solute atoms Weak (see ) Gs c / 700 (see ) [5] Deforming particles Small, coherent Weak (see ) 3/2 fr [6] particles CG (see ) b [7] Non-deforming particles Large, incoherent Strong (see ) Gb particles L 2r [1] equals about 0.2 for FCC metals and about 0.4 for BCC metals. [2] ky scales with inherent flow stress and/or shear modulus; therefore ky is generally greater for BCC metals than for FCC metals. [3] Exception to weak hardening occurs for interstitials in BCC metals; the shear distortion interacts with screw dislocations leading to strong hardening. [4] Equation apropos to substitutional atoms; parameter s is empirical, reflecting a combination of size and modulus hardening. [5] Coherent particles can be "strong" in optimally aged materials. [6] Constant C depends on specific mechanism of hardening; parameter relates to hardening mechanism(s). Equation shown applies to early stage precipitation. Late stage precipitation results in saturation hardening. [7] Highly overaged alloys can represent "weak" hardening. SYMBOLS : G shear modulus; b = Burgers vector; dislocation density ; d grain size; c solute atom concentration (at.%); f precipitate volume fraction; r precipitate radius; L spacing between precipitates on slip plane. Table adapted from Courtney, Mechanical Behavior of Materials, 2 nd edition, p. 232.

LECTURE SUMMARY September 30th 2009

LECTURE SUMMARY September 30th 2009 LECTURE SUMMARY September 30 th 2009 Key Lecture Topics Crystal Structures in Relation to Slip Systems Resolved Shear Stress Using a Stereographic Projection to Determine the Active Slip System Slip Planes

More information

Chapter Outline Dislocations and Strengthening Mechanisms

Chapter Outline Dislocations and Strengthening Mechanisms Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip

More information

Material Deformations. Academic Resource Center

Material Deformations. Academic Resource Center Material Deformations Academic Resource Center Agenda Origin of deformations Deformations & dislocations Dislocation motion Slip systems Stresses involved with deformation Deformation by twinning Origin

More information

Lösungen Übung Verformung

Lösungen Übung Verformung Lösungen Übung Verformung 1. (a) What is the meaning of T G? (b) To which materials does it apply? (c) What effect does it have on the toughness and on the stress- strain diagram? 2. Name the four main

More information

Chapter Outline Dislocations and Strengthening Mechanisms

Chapter Outline Dislocations and Strengthening Mechanisms Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip

More information

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the

More information

CHAPTER 7: DISLOCATIONS AND STRENGTHENING

CHAPTER 7: DISLOCATIONS AND STRENGTHENING CHAPTER 7: DISLOCATIONS AND STRENGTHENING ISSUES TO ADDRESS... Why are dislocations observed primarily in metals and alloys? Mech 221 - Notes 7 1 DISLOCATION MOTION Produces plastic deformation, in crystalline

More information

x100 A o Percent cold work = %CW = A o A d Yield Stress Work Hardening Why? Cell Structures Pattern Formation

x100 A o Percent cold work = %CW = A o A d Yield Stress Work Hardening Why? Cell Structures Pattern Formation Work Hardening Dislocations interact with each other and assume configurations that restrict the movement of other dislocations. As the dislocation density increases there is an increase in the flow stress

More information

Lecture 18 Strain Hardening And Recrystallization

Lecture 18 Strain Hardening And Recrystallization -138- Lecture 18 Strain Hardening And Recrystallization Strain Hardening We have previously seen that the flow stress (the stress necessary to produce a certain plastic strain rate) increases with increasing

More information

CHAPTER 7 DISLOCATIONS AND STRENGTHENING MECHANISMS PROBLEM SOLUTIONS

CHAPTER 7 DISLOCATIONS AND STRENGTHENING MECHANISMS PROBLEM SOLUTIONS 7-1 CHAPTER 7 DISLOCATIONS AND STRENGTHENING MECHANISMS PROBLEM SOLUTIONS Basic Concepts of Dislocations Characteristics of Dislocations 7.1 The dislocation density is just the total dislocation length

More information

Defects Introduction. Bonding + Structure + Defects. Properties

Defects Introduction. Bonding + Structure + Defects. Properties Defects Introduction Bonding + Structure + Defects Properties The processing determines the defects Composition Bonding type Structure of Crystalline Processing factors Defects Microstructure Types of

More information

Dislocation Plasticity: Overview

Dislocation Plasticity: Overview Dislocation Plasticity: Overview 1. DISLOCATIONS AND PLASTIC DEFORMATION An arbitrary deformation of a material can always be described as the sum of a change in volume and a change in shape at constant

More information

Tensile Testing. Objectives

Tensile Testing. Objectives Laboratory 1 Tensile Testing Objectives Students are required to understand the principle of a uniaxial tensile testing and gain their practices on operating the tensile testing machine. Students are able

More information

Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige

Ch. 4: Imperfections in Solids Part 1. Dr. Feras Fraige Ch. 4: Imperfections in Solids Part 1 Dr. Feras Fraige Outline Defects in Solids 0D, Point defects vacancies Interstitials impurities, weight and atomic composition 1D, Dislocations edge screw 2D, Grain

More information

Dislocation theory. Subjects of interest

Dislocation theory. Subjects of interest Chapter 5 Dislocation theory Subjects of interest Introduction/Objectives Observation of dislocation Burgers vector and the dislocation loop Dislocation in the FCC, HCP and BCC lattice Stress fields and

More information

Materials Issues in Fatigue and Fracture

Materials Issues in Fatigue and Fracture Materials Issues in Fatigue and Fracture 5.1 Fundamental Concepts 5.2 Ensuring Infinite Life 5.3 Finite Life 5.4 Summary FCP 1 5.1 Fundamental Concepts Structural metals Process of fatigue A simple view

More information

CHAPTER 4 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS

CHAPTER 4 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS 4-1 CHAPTER 4 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 4.1 In order to compute the fraction of atom sites that are vacant in copper at 1357 K, we must employ Equation

More information

Chapter Outline. Mechanical Properties of Metals How do metals respond to external loads?

Chapter Outline. Mechanical Properties of Metals How do metals respond to external loads? Mechanical Properties of Metals How do metals respond to external loads? Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility

More information

Microscopy and Nanoindentation. Combining Orientation Imaging. to investigate localized. deformation behaviour. Felix Reinauer

Microscopy and Nanoindentation. Combining Orientation Imaging. to investigate localized. deformation behaviour. Felix Reinauer Combining Orientation Imaging Microscopy and Nanoindentation to investigate localized deformation behaviour Felix Reinauer René de Kloe Matt Nowell Introduction Anisotropy in crystalline materials Presentation

More information

Experiment: Crystal Structure Analysis in Engineering Materials

Experiment: Crystal Structure Analysis in Engineering Materials Experiment: Crystal Structure Analysis in Engineering Materials Objective The purpose of this experiment is to introduce students to the use of X-ray diffraction techniques for investigating various types

More information

ME 612 Metal Forming and Theory of Plasticity. 1. Introduction

ME 612 Metal Forming and Theory of Plasticity. 1. Introduction Metal Forming and Theory of Plasticity Yrd.Doç. e mail: azsenalp@gyte.edu.tr Makine Mühendisliği Bölümü Gebze Yüksek Teknoloji Enstitüsü In general, it is possible to evaluate metal forming operations

More information

Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010

Materials Science and Engineering Department MSE , Sample Test #1, Spring 2010 Materials Science and Engineering Department MSE 200-001, Sample Test #1, Spring 2010 ID number First letter of your last name: Name: No notes, books, or information stored in calculator memories may be

More information

Strengthening. Mechanisms of strengthening in single-phase metals: grain-size reduction solid-solution alloying strain hardening

Strengthening. Mechanisms of strengthening in single-phase metals: grain-size reduction solid-solution alloying strain hardening Strengthening The ability of a metal to deform depends on the ability of dislocations to move Restricting dislocation motion makes the material stronger Mechanisms of strengthening in single-phase metals:

More information

Fatigue :Failure under fluctuating / cyclic stress

Fatigue :Failure under fluctuating / cyclic stress Fatigue :Failure under fluctuating / cyclic stress Under fluctuating / cyclic stresses, failure can occur at loads considerably lower than tensile or yield strengths of material under a static load: Fatigue

More information

Size effects. Lecture 6 OUTLINE

Size effects. Lecture 6 OUTLINE Size effects 1 MTX9100 Nanomaterials Lecture 6 OUTLINE -Why does size influence the material s properties? -How does size influence the material s performance? -Why are properties of nanoscale objects

More information

Martensite in Steels

Martensite in Steels Materials Science & Metallurgy http://www.msm.cam.ac.uk/phase-trans/2002/martensite.html H. K. D. H. Bhadeshia Martensite in Steels The name martensite is after the German scientist Martens. It was used

More information

The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C. = 2(sphere volume) = 2 = V C = 4R

The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C. = 2(sphere volume) = 2 = V C = 4R 3.5 Show that the atomic packing factor for BCC is 0.68. The atomic packing factor is defined as the ratio of sphere volume to the total unit cell volume, or APF = V S V C Since there are two spheres associated

More information

Chapter Outline. Diffusion - how do atoms move through solids?

Chapter Outline. Diffusion - how do atoms move through solids? Chapter Outline iffusion - how do atoms move through solids? iffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities The mathematics of diffusion Steady-state diffusion (Fick s first law)

More information

Chapter Outline. How do atoms arrange themselves to form solids?

Chapter Outline. How do atoms arrange themselves to form solids? Chapter Outline How do atoms arrange themselves to form solids? Fundamental concepts and language Unit cells Crystal structures Simple cubic Face-centered cubic Body-centered cubic Hexagonal close-packed

More information

Concepts of Stress and Strain

Concepts of Stress and Strain CHAPTER 6 MECHANICAL PROPERTIES OF METALS PROBLEM SOLUTIONS Concepts of Stress and Strain 6.4 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa (15.5 10 6 psi) and an original

More information

Fatigue Testing. Objectives

Fatigue Testing. Objectives Laboratory 8 Fatigue Testing Objectives Students are required to understand principle of fatigue testing as well as practice how to operate the fatigue testing machine in a reverse loading manner. Students

More information

Activated states for cross-slip at screw dislocation intersections in face-centered cubic nickel and copper via atomistic simulation

Activated states for cross-slip at screw dislocation intersections in face-centered cubic nickel and copper via atomistic simulation Available online at www.sciencedirect.com Acta Materialia 58 (2010) 5547 5557 www.elsevier.com/locate/actamat Activated states for cross-slip at screw dislocation intersections in face-centered cubic nickel

More information

σ y ( ε f, σ f ) ( ε f

σ y ( ε f, σ f ) ( ε f Typical stress-strain curves for mild steel and aluminum alloy from tensile tests L L( 1 + ε) A = --- A u u 0 1 E l mild steel fracture u ( ε f, f ) ( ε f, f ) ε 0 ε 0.2 = 0.002 aluminum alloy fracture

More information

Mechanical properties of twin lamella copper: Preliminary studies

Mechanical properties of twin lamella copper: Preliminary studies : Preliminary studies Markus J. Buehler Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, Abstract. The study of the mechanical properties of materials at nano-

More information

Chapter 5: Diffusion. 5.1 Steady-State Diffusion

Chapter 5: Diffusion. 5.1 Steady-State Diffusion : Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process

More information

MSE 528 - PRECIPITATION HARDENING IN 7075 ALUMINUM ALLOY

MSE 528 - PRECIPITATION HARDENING IN 7075 ALUMINUM ALLOY MSE 528 - PRECIPITATION HARDENING IN 7075 ALUMINUM ALLOY Objective To study the time and temperature variations in the hardness and electrical conductivity of Al-Zn-Mg-Cu high strength alloy on isothermal

More information

v kt = N A ρ Au exp (

v kt = N A ρ Au exp ( 4-2 4.2 Determination of the number of vacancies per cubic meter in gold at 900 C (1173 K) requires the utilization of Equations 4.1 and 4.2 as follows: N v N exp Q v N A ρ Au kt A Au exp Q v kt (6.023

More information

Adam Zaborski handouts for Afghans

Adam Zaborski handouts for Afghans Tensile test Adam Zaborski handouts for Afghans Outline Tensile test purpose Universal testing machines and test specimens Stress-strain diagram Mild steel : proportional stage, elastic limit, yielding

More information

Solid Mechanics. Stress. What you ll learn: Motivation

Solid Mechanics. Stress. What you ll learn: Motivation Solid Mechanics Stress What you ll learn: What is stress? Why stress is important? What are normal and shear stresses? What is strain? Hooke s law (relationship between stress and strain) Stress strain

More information

Mechanical Behavior of Materials Course Notes, 2 nd Edition

Mechanical Behavior of Materials Course Notes, 2 nd Edition Mechanical Behavior of Materials Course Notes, 2 nd Edition Prof. Mark L. Weaver Department of Metallurgical & Materials Engineering A129K Bevill Building The University of Alabama Tuscaloosa, AL 35487-0202

More information

14:635:407:02 Homework III Solutions

14:635:407:02 Homework III Solutions 14:635:407:0 Homework III Solutions 4.1 Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 37 C (600 K). Assume an energy for vacancy formation of 0.55 ev/atom.

More information

Torsion Tests. Subjects of interest

Torsion Tests. Subjects of interest Chapter 10 Torsion Tests Subjects of interest Introduction/Objectives Mechanical properties in torsion Torsional stresses for large plastic strains Type of torsion failures Torsion test vs.tension test

More information

Modern Construction Materials Prof. Ravindra Gettu Department of Civil Engineering Indian Institute of Technology, Madras

Modern Construction Materials Prof. Ravindra Gettu Department of Civil Engineering Indian Institute of Technology, Madras Modern Construction Materials Prof. Ravindra Gettu Department of Civil Engineering Indian Institute of Technology, Madras Module - 2 Lecture - 2 Part 2 of 2 Review of Atomic Bonding II We will continue

More information

Fundamentals of grain boundaries and grain boundary migration

Fundamentals of grain boundaries and grain boundary migration 1. Fundamentals of grain boundaries and grain boundary migration 1.1. Introduction The properties of crystalline metallic materials are determined by their deviation from a perfect crystal lattice, which

More information

Mechanical Properties

Mechanical Properties Mechanical Properties Hardness Hardness can be defined as resistance to deformation or indentation or resistance to scratch. Hardness Indentation Scratch Rebound Indentation hardness is of particular interest

More information

Chapter Outline. Defects Introduction (I)

Chapter Outline. Defects Introduction (I) Crystals are like people, it is the defects in them which tend to make them interesting! - Colin Humphreys. Defects in Solids Chapter Outline 0D, Point defects vacancies interstitials impurities, weight

More information

Dynamic Dislocation Mechanisms for the Anomalous Slip in a Single-Crystal BCC Metal Oriented for Single Slip

Dynamic Dislocation Mechanisms for the Anomalous Slip in a Single-Crystal BCC Metal Oriented for Single Slip UCRL-TR-227296 LAWRENCE LIVERMORE NATIONAL LABORATORY Dynamic Dislocation Mechanisms for the Anomalous Slip in a Single-Crystal BCC Metal Oriented for Single Slip L. Hsiung January 12, 2007 This document

More information

STRAIN ENERGY DENSITY (strain energy per unit volume)

STRAIN ENERGY DENSITY (strain energy per unit volume) STRAIN ENERGY DENSITY (strain energy per unit volume) For ductile metals and alloys, according to the Maximum Shear Stress failure theory (aka Tresca ) the only factor that affects dislocation slip is

More information

The stored energy of cold work: Predictions from discrete dislocation plasticity

The stored energy of cold work: Predictions from discrete dislocation plasticity Acta Materialia 53 (2005) 4765 4779 www.actamat-journals.com The stored energy of cold work: Predictions from discrete dislocation plasticity A.A. Benzerga a, *, Y. Bréchet b, A. Needleman c, E. Van der

More information

EFFECT OF SEVERE PLASTIC DEFORMATION ON STRUCTURE AND PROPERTIES OF AUSTENITIC AISI 316 GRADE STEEL

EFFECT OF SEVERE PLASTIC DEFORMATION ON STRUCTURE AND PROPERTIES OF AUSTENITIC AISI 316 GRADE STEEL EFFECT OF SEVERE PLASTIC DEFORMATION ON STRUCTURE AND PROPERTIES OF AUSTENITIC AISI 316 GRADE STEEL Ladislav KANDER a, Miroslav GREGER b a MATERIÁLOVÝ A METALURGICKÝ VÝZKUM, s.r.o., Ostrava, Czech Republic,

More information

Lecture 14. Chapter 8-1

Lecture 14. Chapter 8-1 Lecture 14 Fatigue & Creep in Engineering Materials (Chapter 8) Chapter 8-1 Fatigue Fatigue = failure under applied cyclic stress. specimen compression on top bearing bearing motor counter flex coupling

More information

Crystal Defects p. 2. Point Defects: Vacancies. Department of Materials Science and Engineering University of Virginia. Lecturer: Leonid V.

Crystal Defects p. 2. Point Defects: Vacancies. Department of Materials Science and Engineering University of Virginia. Lecturer: Leonid V. Crystal Defects p. 1 A two-dimensional representation of a perfect single crystal with regular arrangement of atoms. But nothing is perfect, and structures of real materials can be better represented by

More information

Solution for Homework #1

Solution for Homework #1 Solution for Homework #1 Chapter 2: Multiple Choice Questions (2.5, 2.6, 2.8, 2.11) 2.5 Which of the following bond types are classified as primary bonds (more than one)? (a) covalent bonding, (b) hydrogen

More information

EFFECTS OF STRAIN RATE ON WORK HARDENING OF HSLA AND Ti-IF STEELS

EFFECTS OF STRAIN RATE ON WORK HARDENING OF HSLA AND Ti-IF STEELS METALLURGY AND FOUNDRY ENGINEERING Vol. 32, 2006, No. 1 Monika Stefañska-K¹dziela *, Janusz Majta **, Krzysztof Muszka *** EFFECTS OF STRAIN RATE ON WORK HARDENING OF HSLA AND Ti-IF STEELS Notation: A

More information

ORIENTATION CHARACTERISTICS OF THE MICROSTRUCTURE OF MATERIALS

ORIENTATION CHARACTERISTICS OF THE MICROSTRUCTURE OF MATERIALS ORIENTATION CHARACTERISTICS OF THE MICROSTRUCTURE OF MATERIALS K. Sztwiertnia Polish Academy of Sciences, Institute of Metallurgy and Materials Science, 25 Reymonta St., 30-059 Krakow, Poland MMN 2009

More information

Uniaxial Tension and Compression Testing of Materials. Nikita Khlystov Daniel Lizardo Keisuke Matsushita Jennie Zheng

Uniaxial Tension and Compression Testing of Materials. Nikita Khlystov Daniel Lizardo Keisuke Matsushita Jennie Zheng Uniaxial Tension and Compression Testing of Materials Nikita Khlystov Daniel Lizardo Keisuke Matsushita Jennie Zheng 3.032 Lab Report September 25, 2013 I. Introduction Understanding material mechanics

More information

Torsion Testing. Objectives

Torsion Testing. Objectives Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials

More information

, to obtain a way to calculate stress from the energy function U(r).

, to obtain a way to calculate stress from the energy function U(r). BIOEN 36 013 LECTURE : MOLECULAR BASIS OF ELASTICITY Estimating Young s Modulus from Bond Energies and Structures First we consider solids, which include mostly nonbiological materials, such as metals,

More information

THE WAY TO SOMEWHERE. Sub-topics. Diffusion Diffusion processes in industry

THE WAY TO SOMEWHERE. Sub-topics. Diffusion Diffusion processes in industry THE WAY TO SOMEWHERE Sub-topics 1 Diffusion Diffusion processes in industry RATE PROCESSES IN SOLIDS At any temperature different from absolute zero all atoms, irrespective of their state of aggregation

More information

Stress Strain Relationships

Stress Strain Relationships Stress Strain Relationships Tensile Testing One basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. These properties relate the stresses to the

More information

Relevant Reading for this Lecture... Pages 83-87.

Relevant Reading for this Lecture... Pages 83-87. LECTURE #06 Chapter 3: X-ray Diffraction and Crystal Structure Determination Learning Objectives To describe crystals in terms of the stacking of planes. How to use a dot product to solve for the angles

More information

Question 6.5: A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm

Question 6.5: A steel bar 100 mm (4.0 in.) long and having a square cross section 20 mm 14:440:407 Ch6 Question 6.3: A specimen of aluminum having a rectangular cross section 10 mm 12.7 mm (0.4 in. 0.5 in.) is pulled in tension with 35,500 N (8000 lb f ) force, producing only elastic deformation.

More information

Numerical Simulation of Earth Materials

Numerical Simulation of Earth Materials Numerical Simulation of Earth Materials Summary of part and current research in materials simulation Mark Jessell Université Paul Sabatier, Toulouse How hard can it be? Octachloropropane Grain boundary

More information

Pore pressure. Ordinary space

Pore pressure. Ordinary space Fault Mechanics Laboratory Pore pressure scale Lowers normal stress, moves stress circle to left Doesn Doesn t change shear Deviatoric stress not affected This example: failure will be by tensile cracks

More information

Laterally Loaded Piles

Laterally Loaded Piles Laterally Loaded Piles 1 Soil Response Modelled by p-y Curves In order to properly analyze a laterally loaded pile foundation in soil/rock, a nonlinear relationship needs to be applied that provides soil

More information

Chapter Outline: Phase Transformations in Metals

Chapter Outline: Phase Transformations in Metals Chapter Outline: Phase Transformations in Metals Heat Treatment (time and temperature) Microstructure Mechanical Properties Kinetics of phase transformations Multiphase Transformations Phase transformations

More information

Heat Treatment of Aluminum Foundry Alloys. Fred Major Rio Tinto Alcan

Heat Treatment of Aluminum Foundry Alloys. Fred Major Rio Tinto Alcan Heat Treatment of Aluminum Foundry Alloys Fred Major Rio Tinto Alcan OUTLINE Basics of Heat Treatment (What is happening to the metal at each step). Atomic Structure of Aluminum Deformation Mechanisms

More information

Mechanical Properties - Stresses & Strains

Mechanical Properties - Stresses & Strains Mechanical Properties - Stresses & Strains Types of Deformation : Elasic Plastic Anelastic Elastic deformation is defined as instantaneous recoverable deformation Hooke's law : For tensile loading, σ =

More information

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N)

Weight The weight of an object is defined as the gravitational force acting on the object. Unit: Newton (N) Gravitational Field A gravitational field as a region in which an object experiences a force due to gravitational attraction Gravitational Field Strength The gravitational field strength at a point in

More information

METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING

METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING Met E 206 MATERIALS LABORATORY EXPERIMENT 1 Prof. Dr. Rıza GÜRBÜZ Res. Assist. Gül ÇEVİK (Room: B-306) INTRODUCTION TENSION TEST Mechanical testing

More information

Yield Criteria for Ductile Materials and Fracture Mechanics of Brittle Materials. τ xy 2σ y. σ x 3. τ yz 2σ z 3. ) 2 + ( σ 3. σ 3

Yield Criteria for Ductile Materials and Fracture Mechanics of Brittle Materials. τ xy 2σ y. σ x 3. τ yz 2σ z 3. ) 2 + ( σ 3. σ 3 Yield Criteria for Ductile Materials and Fracture Mechanics of Brittle Materials Brittle materials are materials that display Hookean behavior (linear relationship between stress and strain) and which

More information

HW 10. = 3.3 GPa (483,000 psi)

HW 10. = 3.3 GPa (483,000 psi) HW 10 Problem 15.1 Elastic modulus and tensile strength of poly(methyl methacrylate) at room temperature [20 C (68 F)]. Compare these with the corresponding values in Table 15.1. Figure 15.3 is accurate;

More information

Dislocation slip or deformation twinning: confining pressure makes a difference

Dislocation slip or deformation twinning: confining pressure makes a difference Materials Science and Engineering A 387 389 (2004) 840 844 Dislocation slip or deformation twinning: confining pressure makes a difference Dong-Sheng Xu a,, Jin-Peng Chang b,juli c, Rui Yang a, Dong Li

More information

In order to solve this problem it is first necessary to use Equation 5.5: x 2 Dt. = 1 erf. = 1.30, and x = 2 mm = 2 10-3 m. Thus,

In order to solve this problem it is first necessary to use Equation 5.5: x 2 Dt. = 1 erf. = 1.30, and x = 2 mm = 2 10-3 m. Thus, 5.3 (a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion. Solution (a) With vacancy diffusion,

More information

What is Manufacturing?

What is Manufacturing? MECH 421/6511 Shaping of Metals and Plastics DEPT. OF MECH. AND IND. ENG. MECH 421/6511 Shaping of Metals and Plastics LECTURES: Mon-Wed ER- 511-9 at 4:15 to 5:30 pm FACULTY: Dr. Mamoun Medraj e-mail:

More information

Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.

Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials. Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity

More information

Lecture: 33. Solidification of Weld Metal

Lecture: 33. Solidification of Weld Metal Lecture: 33 Solidification of Weld Metal This chapter presents common solidification mechanisms observed in weld metal and different modes of solidification. Influence of welding speed and heat input on

More information

Phase Transformations in Metals and Alloys

Phase Transformations in Metals and Alloys Phase Transformations in Metals and Alloys THIRD EDITION DAVID A. PORTER, KENNETH E. EASTERLING, and MOHAMED Y. SHERIF ( г йс) CRC Press ^ ^ ) Taylor & Francis Group Boca Raton London New York CRC Press

More information

Ajit Kumar Patra (Autor) Crystal structure, anisotropy and spin reorientation transition of highly coercive, epitaxial Pr-Co films

Ajit Kumar Patra (Autor) Crystal structure, anisotropy and spin reorientation transition of highly coercive, epitaxial Pr-Co films Ajit Kumar Patra (Autor) Crystal structure, anisotropy and spin reorientation transition of highly coercive, epitaxial Pr-Co films https://cuvillier.de/de/shop/publications/1306 Copyright: Cuvillier Verlag,

More information

MAL 201E: Materials Science. COURSE MATERIALS (with text) GRADING 25.09.2012 COURSE SCHEDULE

MAL 201E: Materials Science. COURSE MATERIALS (with text) GRADING 25.09.2012 COURSE SCHEDULE MAL 201E: Materials Science Course Objective... Introduce fundamental concepts in Materials Science You will learn about: material structure how structure dictates properties how processing can change

More information

Wafer Manufacturing. Reading Assignments: Plummer, Chap 3.1~3.4

Wafer Manufacturing. Reading Assignments: Plummer, Chap 3.1~3.4 Wafer Manufacturing Reading Assignments: Plummer, Chap 3.1~3.4 1 Periodic Table Roman letters give valence of the Elements 2 Why Silicon? First transistor, Shockley, Bardeen, Brattain1947 Made by Germanium

More information

Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield

Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield MTE 585 Oxidation of Materials Part 1 Ref. Ch. 11 in Superalloys II Ch. 8 in Khanna Ch. 14 in Tien & Caulfield Introduction To illustrate the case of high temperature oxidation, we will use Ni-base superalloys.

More information

SPECIFICATIONS, LOADS, AND METHODS OF DESIGN

SPECIFICATIONS, LOADS, AND METHODS OF DESIGN CHAPTER Structural Steel Design LRFD Method Third Edition SPECIFICATIONS, LOADS, AND METHODS OF DESIGN A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II Structural

More information

M n = (DP)m = (25,000)(104.14 g/mol) = 2.60! 10 6 g/mol

M n = (DP)m = (25,000)(104.14 g/mol) = 2.60! 10 6 g/mol 14.4 (a) Compute the repeat unit molecular weight of polystyrene. (b) Compute the number-average molecular weight for a polystyrene for which the degree of polymerization is 25,000. (a) The repeat unit

More information

Chapter 3: Structure of Metals and Ceramics. Chapter 3: Structure of Metals and Ceramics. Learning Objective

Chapter 3: Structure of Metals and Ceramics. Chapter 3: Structure of Metals and Ceramics. Learning Objective Chapter 3: Structure of Metals and Ceramics Chapter 3: Structure of Metals and Ceramics Goals Define basic terms and give examples of each: Lattice Basis Atoms (Decorations or Motifs) Crystal Structure

More information

A R C H I V E S O F M E T A L L U R G Y A N D M A T E R I A L S Volume 57 2012 Issue 3 DOI: 10.2478/v10172-012-0095-3

A R C H I V E S O F M E T A L L U R G Y A N D M A T E R I A L S Volume 57 2012 Issue 3 DOI: 10.2478/v10172-012-0095-3 A R C H I V E S O F M E T A L L U R G Y A N D M A T E R I A L S Volume 57 2012 Issue 3 DOI: 10.2478/v10172-012-0095-3 K. TOPOLSKI, H. GARBACZ, P. WIECIŃSKI, W. PACHLA, K.J. KURZYDŁOWSKI MECHANICAL PROPERTIES

More information

9. TIME DEPENDENT BEHAVIOUR: CYCLIC FATIGUE

9. TIME DEPENDENT BEHAVIOUR: CYCLIC FATIGUE 9. TIME DEPENDENT BEHAVIOUR: CYCLIC FATIGUE A machine part or structure will, if improperly designed and subjected to a repeated reversal or removal of an applied load, fail at a stress much lower than

More information

Tension fracture behaviors of welded joints in X70 steel pipeline

Tension fracture behaviors of welded joints in X70 steel pipeline THEORETICAL & APPLIED MECHANICS LETTERS 1, 031008 (2011) Tension fracture behaviors of welded joints in X70 steel pipeline Dejun Kong, a) Yongzhong Wu, Dan Long, and Chaozheng Zhou College of Mechanical

More information

COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS

COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 7, Issue 2, March-April 2016, pp. 30 52, Article ID: IJARET_07_02_004 Available online at http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=7&itype=2

More information

CONSOLIDATION AND HIGH STRAIN RATE MECHANICAL BEHAVIOR OF NANOCRYSTALLINE TANTALUM POWDER

CONSOLIDATION AND HIGH STRAIN RATE MECHANICAL BEHAVIOR OF NANOCRYSTALLINE TANTALUM POWDER CONSOLIDATION AND HIGH STRAIN RATE MECHANICAL BEHAVIOR OF NANOCRYSTALLINE TANTALUM POWDER Sang H. Yoo, T.S. Sudarshan, Krupa Sethuram Materials Modification Inc, 2929-P1 Eskridge Rd, Fairfax, VA, 22031

More information

Iron-Carbon Phase Diagram (a review) see Callister Chapter 9

Iron-Carbon Phase Diagram (a review) see Callister Chapter 9 Iron-Carbon Phase Diagram (a review) see Callister Chapter 9 University of Tennessee, Dept. of Materials Science and Engineering 1 The Iron Iron Carbide (Fe Fe 3 C) Phase Diagram In their simplest form,

More information

10.1 Powder mechanics

10.1 Powder mechanics Fluid and Particulate systems 424514 /2014 POWDER MECHANICS & POWDER FLOW TESTING 10 Ron Zevenhoven ÅA Thermal and Flow Engineering ron.zevenhoven@abo.fi 10.1 Powder mechanics RoNz 2/38 Types of flow of

More information

Chapter 22: Electric Flux and Gauss s Law

Chapter 22: Electric Flux and Gauss s Law 22.1 ntroduction We have seen in chapter 21 that determining the electric field of a continuous charge distribution can become very complicated for some charge distributions. t would be desirable if we

More information

Hardness of Electrodeposited Nano-Nickel Revisited

Hardness of Electrodeposited Nano-Nickel Revisited Hardness of Electrodeposited Nano-Nickel Revisited by Bill Tsz Fai Tang A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Department of Materials Science

More information

Bending, Forming and Flexing Printed Circuits

Bending, Forming and Flexing Printed Circuits Bending, Forming and Flexing Printed Circuits John Coonrod Rogers Corporation Introduction: In the printed circuit board industry there are generally two main types of circuit boards; there are rigid printed

More information

FATIGUE CONSIDERATION IN DESIGN

FATIGUE CONSIDERATION IN DESIGN FATIGUE CONSIDERATION IN DESIGN OBJECTIVES AND SCOPE In this module we will be discussing on design aspects related to fatigue failure, an important mode of failure in engineering components. Fatigue failure

More information

1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids 1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

More information

LABORATORY EXPERIMENTS TESTING OF MATERIALS

LABORATORY EXPERIMENTS TESTING OF MATERIALS LABORATORY EXPERIMENTS TESTING OF MATERIALS 1. TENSION TEST: INTRODUCTION & THEORY The tension test is the most commonly used method to evaluate the mechanical properties of metals. Its main objective

More information

Chapter 8. Phase Diagrams

Chapter 8. Phase Diagrams Phase Diagrams A phase in a material is a region that differ in its microstructure and or composition from another region Al Al 2 CuMg H 2 O(solid, ice) in H 2 O (liquid) 2 phases homogeneous in crystal

More information

Structural Integrity Analysis

Structural Integrity Analysis Structural Integrity Analysis 1. STRESS CONCENTRATION Igor Kokcharov 1.1 STRESSES AND CONCENTRATORS 1.1.1 Stress An applied external force F causes inner forces in the carrying structure. Inner forces

More information